Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property

Abstract

We study Chern characters and the assembly mapping for free actions using the framework of geometric $K$-homology. The focus is on the relative groups associated with a group homomorphism $\varphi :{\Gamma }_1\to {\Gamma }_2$ along with applications to Novikov type properties. In particular, we prove a relative strong Novikov property for homomorphisms of hyperbolic groups and a relative strong ${\ell }^1$-Novikov property for polynomially bounded homomorphisms of groups with polynomially bounded cohomology in $\C$. As a corollary, relative higher signatures on a manifold with boundary $W$, with ${\pi }_1(\partial W)\to {\pi }_1(W)$ belonging to the class above, are homotopy invariant.

32 pages, accepted in Münster Journal of Mathematics

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• Operator *-correspondences in analysis and geometry
• Positive scalar curvature and a new index theory for noncompact manifolds
• Adiabatic groupoids and secondary invariants in K-theory
• Relative geometric assembly and mapping cones, Part I: The geometric model and applications

Cited by in corpus (1)

• Relative geometric assembly and mapping cones, Part I: The geometric model and applications